Question

A point is translated on the coordinate plane from (2,−5)%0D%0A(%0D%0A2%0D%0A,%0D%0A−%0D%0A5%0D%0A)%0D%0A to (2,−6)%0D%0A(%0D%0A2%0D%0A,%0D%0A−%0D%0A6%0D%0A)%0D%0A. Create a function to show this translation. Which function shows the appropriate translation?(1 point)%0D%0AResponses%0D%0A%0D%0Af(x)=x−1%0D%0A𝑓%0D%0A(%0D%0A𝑥%0D%0A)%0D%0A=%0D%0A𝑥%0D%0A−%0D%0A1%0D%0Af left parenthesis x right parenthesis equals x minus 1%0D%0A%0D%0Ag(y)=y−1%0D%0A𝑔%0D%0A(%0D%0A𝑦%0D%0A)%0D%0A=%0D%0A𝑦%0D%0A−%0D%0A1%0D%0Ag left parenthesis y right parenthesis equals y minus 1%0D%0A%0D%0Ag(y)=y+1%0D%0A𝑔%0D%0A(%0D%0A𝑦%0D%0A)%0D%0A=%0D%0A𝑦%0D%0A+%0D%0A1%0D%0Ag left parenthesis y right parenthesis equals y plus 1%0D%0A%0D%0Ag(y)=y

Answer 1

To translate the point \((2, -5)\) to \((2, -6)\), we are changing the \(y\)-coordinate from \(-5\) to \(-6\). This means we are subtracting 1 from the \(y\)-value.

The appropriate translation function can be represented as:

\[
g(y) = y - 1
\]

Here's the reasoning for the options provided:

1. **\(f(x) = x - 1\)**: This function modifies the \(x\)-coordinate, which does not apply to our translation since only the \(y\)-coordinate is changing.

2. **\(g(y) = y - 1\)**: This is the correct function because it correctly represents the change in the \(y\)-coordinate by subtracting 1 (moving downwards by 1 unit).

3. **\(g(y) = y + 1\)**: This would translate the point upwards, which is not the case here.

4. **\(g(y) = y\)**: This means there is no change in the \(y\)-coordinate, which is incorrect.

The correct response is:

\[
g(y) = y - 1
\]